
Numerical Methods for Timedependent PDE's
Credits 
8 credit points 
Instructors 
Zegeling, P. (Universiteit Utrecht) 
Email 
P.A.Zegeling@uu.nl 
Prerequisites 
Basic knowledge of analysis, numerical analysis and some programming experience. 
Aim 
To provide theoretical insight in, and to develop some practical skills for, numerical solution methods for evolutionary (timedependent) partial differential equations (PDEs). Particular emphasis lies on finite difference and finite volume methods for parabolic and hyperbolic PDEs. 
Description 
The following topics will be treated: * Classification of PDEs, basic examples and applications * Introduction to finite differences (FDs) & basic theory: convergence, consistency and stability * The Lax theorem and Von Neumann stability analysis * Dispersion, dissipation and modified PDEs * FDs for parabolic equations in one and two space dimensions * FDs and finite volume methods for hyperbolic equations (wavetype equations) * The methodoflines approach * Nonuniform and adaptive moving grids * Higherorder and spectral methods * Nonstandard finitedifferences * Treatment of special PDE models, such as advectiondiffusionreaction equations, fractionalorder, higherorder and Hamiltonian PDEs 
Organization 
Lectures (2x 45 minutes) & excercise classes (1x 45 minutes). 
Examination 
The final grade is based on homework assigments & programming assignments & a final test. 
Literature 
Handouts & the books (both optional) W. Hundsdorfer & J.G. Verwer, Numerical Solution of TimeDependent AdvectionDiffusionReaction Equations (Springer Series in Computational Mathematics, ISSN: 01793632) and Uri M. Ascher, Numerical Methods for Evolutionary Differential Equations (SIAM, 2008, Softcover, ISBN 9780898716528). 
